Goals from Simone Zaza, Nicola Sansone and Domenico Berardi sent Inter to a second successive Serie A defeat, and their first at the hands of Sassuolo.
Mauro Icardi struck to get Inter back in the fixture at 2-1, before Sansone and Isaac Donkor were sent off, but Berardi secured victory for the hosts.
When Inter's players approached their fans after the final whistle arguments broke out between them, with some supporters throwing shirts back at the players in disgust at their performance.
"Clearly there is some psychological fragility, as at the slightest difficulty they see everything negative," said Mancini.
"However, we absolutely did not deserve to lose this game.
"The players want to win and see they are unlucky hitting the woodwork, so naturally that affects their confidence. It can also explain the tension at the end.
"I am very sorry for the boys and for the fans. Every now and then you can create misunderstandings but I hope everything will be resolved soon because we need our supporters."
Mancini rued mistakes in the Inter defence during the first half as they gifted Sassuolo two goals, but remains confident their luck will change.
He added: "Things are going wrong at the moment, but in the first 20 minutes we played the way we needed to.
"Unfortunately in Italy the only thing anyone cares about is the result, so we hope that can improve quickly."
